What am I missing - domains of functions

[Duindorp]

Hi,
I know I am missing something obvious here but just can't understand what I am getting wrong.

I was trying to graph this equation

y=-2*3^(5-x)

It is related to a problem I was working on in Khan Academy - but I went on a tangent of thinking.

When I graph this function using Desmos it looks very much like the domain of the function is x>0. This also seems to match my lessons.

However when I decide to just impose a negative x value, say x=-1 then the function 'appears' to throw out a value.

y=-2*3^(5--1)
y=-2*3⁽⁵⁺¹⁾
y=-2*3⁽⁶⁾
y=-2*729
y=-1458

so for x=-1, y=-1458

Why does this not graph. My below graph seems to indicate -1 is outside the domain of the function? What am I missing - please help this is driving me crazy!!!! (many thanks in advance)

 

[Deleted member 4993]

Hi,
I know I am missing something obvious here but just can't understand what I am getting wrong.

I was trying to graph this equation

y=-2*3^(5-x)

It is related to a problem I was working on in Khan Academy - but I went on a tangent of thinking.

When I graph this function using Desmos it looks very much like the domain of the function is x>0. This also seems to match my lessons.

However when I decide to just impose a negative x value, say x=-1 then the function 'appears' to throw out a value.

y=-2*3^(5--1)
y=-2*3⁽⁵⁺¹⁾
y=-2*3⁽⁶⁾
y=-2*729
y=-1458

so for x=-1, y=-1458

Why does this not graph. My below graph seems to indicate -1 is outside the domain of the function? What am I missing - please help this is driving me crazy!!!! (many thanks in advance)

If you notice, the maximum |y| shown in the graph is 100. At x = 0, |y| = ~500, and that is why it does not show up in your graph. If you plot using wolframalpha.com,

you will see that the given function does not have a y-asymptote. So your analysis is correct. The graph shown by Desmos is correct but misleading.

 

[Ishuda]

Hi,
I know I am missing something obvious here but just can't understand what I am getting wrong.

I was trying to graph this equation

y=-2*3^(5-x)

It is related to a problem I was working on in Khan Academy - but I went on a tangent of thinking. ...

Sometimes an extended domain, such as all real numbers, may be limited to a smaller domain, such as only positive numbers, because that is the only region of interest or region of application. For example, suppose we look at Moore's law which states that the processing power of computers will double about every 18 months. The formula for this is then
P(t) = \(\displaystyle P_0\, 2^{\frac{2}{3} (t\, -\, t_0)}\)
where t₀ is some initial year where the processing power is P₀. Although this 'law' has roughly held from about 1970 to 2010, we would not expect it to hold for 1900 although the formula does give a value for 1900. Thus we might restrict the domain of this function to t about 1970 and greater [and wonder where it might begin to break down].

As Subhotosh Khan indicated, WolframAlpha is a nice site for many things and the plot of your function for x=-3 to x=1 is shown here
http://www.wolframalpha.com/input/?i=plot+-2*e^%285-x%29+from+x%3D-3+to+x%3D1
If interested, you could play around with the from/to numbers to get different appearances. The scale x=0 to x=20 will given something like the Desmos graph